Instructor: Dr. John Tolle
Email: tolle+@andrew.cmu.edu
Office: Wean Hall 6124
Teaching Assistant: Albert Cohen; email: albertc+@andrew.cmu.edu
Questions: If you have questions about homework, please send email to BOTH me and Al. This way, whichever of us receives your message first can respond to it, and this will minimize the time it takes for you to get help.
Fax: The fax number for the Department of Mathematical Sciences at CMU is 412-268-6380. New York students may wish to turn in their homework by fax to get papers back sooner, or simply email it to me if it is in .doc or .pdf format.
Prerequisites: Two semesters of calculus, some background in matrix algebra.
Assignments: There will be four homework assignments. Each comprises 20% of the grade. You are welcome (yea, encouraged) to work together on assignments, but each of you should write up your results separately. Typically, the problems should be worked out in rough form first; during this stage, you may consort with one another. But a second stage should involve you reviewing and refining your arguments to write up in final form; you should do this part independently. Copying another's work in whole or in part will be considered a serious breach of ethics, but merely discussing problem-solving strategy is OK.
We will read your work and mark weak (or incorrect) points in your arguments. We may not always provide detailed written feedback on your work, but model solutions to the exercises will be provided, and because of this, late homework cannot be accepted. On the due date, hand in whatever you've got. (All homeworks are due by 5:30 PM.)
Professor's Appearance: Somewhat haggard.
Teaching Assistant's Appearance: A bit less frightening to small children.
Exam: There will be one in-class exam, given Thursday, August 18 at 5:30 PM. The exam comprises 20% of the grade.
Grading: The exam and each of the assignments is worth 20%; for a final grade of A, your overall average should be 90 or above; 80-89.99 for a B; 70-79.99 for a C; 60-69.99 for a D (but none of you will fall in that range, correct?); and below 60, well ...
Lecture 1: Finite and infinite sets, Countability. (Read Chapters 0 and 1.)
Lecture 2: Limits of functions of one variable,
Algebraic structure of R^n,
Limits of multivariate and vector-valued functions,
Continuity.
(Read Chapter 2.)
Lecture 3: Continuity, Continuity theorems, Differentiability, The algebra of derivatives. (Read Chapters 3 and 4.)
Lecture 4: The chain rule, Mean value theorem, l'Hospital's rule, The Darboux integral. (Read Chapter 5.)
Lecture 5: Integrability theorems, The fundamental theorem of calculus, Convex functions, Jensen's inequality. (Read Chapters 5 and 6.)
Lecture 6: Analytic functions of one variable, Partial derivatives, Analytic multivariate functions, Linear independence, Basis, Dimension. (Read Chapter 7; for most of you, Chapter 8 will probably only require a quick reading or a skimming, because the rudiments of Gauss-Jordan elimination will be reviewed in class; read Chapter 9.)
Lecture 7: Orthogonality, Symmetric matrices, Eigenvalues, Eigenvectors, Eigenspaces, Eigenbases. (Read Chapters 10 and 11.)
Lecture 8: Orthonormal eigenbases for symmetric matrices, Quadratic forms, Positive definiteness.